The path-integral centroid approach has been applied to study the dynamical properties of a flux of protons impinging on a symmetric Eckart barrier. The mean transmission coefficient, transmitted flux, and kinetic energy of transmitted particles have been calculated by path-integral centroid simulations as a function of-temperature, and compared to exact results obtained from the solution of the Schrodinger equation. The studied temperatures cover the crossover from a classical regime, where the barrier crossing is thermally activated, to a quantum regime, where the barrier crossing is dominated by tunneling of low energy particles. We show, in agreement with previous studies, that the centroid density is a central quantity to derive dynamical properties. Moreover, we find that the equilibrium internal energy obtained for the centroid fixed at the barrier top, reproduces closely the difference between the mean kinetic energy of transmitted and incident particles, and it can be used to define a velocity (pre-exponential) factor that improves previous approximations to the transmitted flux, in the whole temperature range above and below the classical-quantum crossover. (C) 1997 American Institute of Physics.